External Harddrive or Xbox Series X

This article explains the difference between using a regular external hard drive versus the custom external storage for the Series S/X- https://news.xbox.com/en-us/2020/09...xbox-series-s-custom-storage-solution-primer/

An external hard drive used on the One will work for the Series S/X, but won't have the exact same performance as the one created for the Series S/X.

If they were to put it a bigger ssd internally the price of the series x would rocket so to keep prices at a reasonable level these 1tb ssd drives sold separately and you only need them to play series x games once the internal ssd is full however you can
still use standard external harddrives to play xbox one 360 and og games from and yoi can also store series x games on them you just cant play the series x games from them so it might mean a little more transfering around of series x games (which will move
much faster than hames move now) so for a fair while you probably wont even need the plug in ssd drive.

Not really...

Xbox Series X games / upgrades / updates has to be installed onto the Series X internal or expansion card SSD,

You can have Xbox One games on your external hard drive that will get an Series X upgrade but the games will need to be transferred to the Series X and then the Series X upgrade will need to be downloaded onto the Series X SSD,

As an example...

I have Marvel Avengers on my external hard drive that will get the Series X upgrade and I will transfer the game over to the Series X SSD ready to download and update the game to the Series X version when available.

Also looks like ill probably be needing an external harddrive to free up more space...any suggestions on a type or brand that works well with the xbox one x?

Something's wrong with your initial statement "500gb Xbox One X" The Xbox One X has a 1tb harddrive.

In answer to your question is no you can't run it from an external drive you will need to get your xbox repaired.